ams (mos) major subject headings (1970) · swanson, c. a. a comparison theorem for eigenfunctions,...

AMS (MOS) MAJOR SUBJECT HEADINGS (1970)

The letters in parentheses indicate groupings which are used in

table of contents of each issue and in the volume index.

00 (H) General

01 (H) History and Biography

02 (E) Logic and Foundations

04 (E) Set Theory

05 (A) Combinatorics

06 (A) Order, Lattices, OrderedAlgebraic Structures

08 (A) General Mathematical

Systems

10 (A) Number Theory

12 (A) Algebraic Number Theory,Field Theory and Polynomials

13 (A) Commutative Rings andAlgebras

14 (A) Algebraic Geometry

15 (A) Linear and Multilinear

Algebra, Matrix Theory

(finite and infinite)

16 (A) Associative Rings andAlgebras

17 (A) Nonassociative Rings and

Algebras

18 (A) Category Theory,

Homological Algebra20 (A) Group Theory and

Generalizations

22 (G) Topological Groups, LieGroups

26 (B) Real Functions28 (B) Measure and Integration

30 (B) Functions of a ComplexVariable

31 (B) Potential Theory32 (B) Several Complex Variables

and Analytic Spaces33 (B) Special Functions34 (B) Ordinary Differential

Equations35 (B) Partial Differential Equations39 (B) Finite Differences and

Functional Equations

40 (B) Sequences, Series,

Summability

41 (B) Approximations and

Expansions

42 (B) Fourier Analysis

43 (B) Abstract Harmonic Analysis

44 (B) Integral Transforms,

Operational Calculus

45 (B) Integral Equations

46 (B) Functional Analysis47 (B) Operator Theory

49 (B) Calculus of Variations andOptimal Control

50 (D) Geometry

52 (D) Convex Sets and Geometric

Inequalities53 (D) Differential Geometry54 (G) General Topology

55 (G) Algebraic Topology

57 (G) Manifolds and Cell Complexes58 (G) Global Analysis, Analysis on

Manifolds

60 (F) Probability Theory and

Stochastic Processes

62 (F) Statistics65 (C) Numerical Analysis

68 (C) Computer Science70 (C) Mechanics of Particles and

Systems

73 (C) Mechanics of Solids76 (C) Fluid Mechanics78 (C) Optics, Electromagnetic

Theory

80 (C) Classical Thermodynamics,

Heat Transfer

81 (C) Quantum Mechanics

82 (C) Statistical Physics, Structure

of Matter83 (C) Relativity85 (C) Astronomy and Astrophysics

86 (C) Geophysics90 (C) Economics, Operations Re-

search, Programming, Games

92 (C) Biology and Behavioral

Sciences

83 (C) Systems, Control

94 (C) Information and Communica-

tion, Circuits, Automata

96 (H) Mathematical Education,

Elementary


Secondary


Collegiate

623

INDEX TO VOLUME 37

SUBJECT INDEX

* Starred items are "Shorter

Notes"

A. Algebra and Number Theory

05. Combinatorics

Howard, F. T. Formulas for the number of binomial coefficients divisible by a

fixed power of a prime, 358."O'Neil, P. V. A short proof of Mac Lane's planarity theorem, 619.

Parker, E. T. Edge coloring numbers of some regular graphs, 423.

06. Order, Lattices, Ordered Algebraic Structures

Hung, H. H. The amalgamation property for G-metric spaces, 53.

Lakser, Harry. Principal congruences of pseudocomplemented distributive lattices,

32.Reynolds, William H. A note on embedding a partially ordered ring in a division

algebra, 37.

Rival, Ivan. Maximal sublattices of finite distributive lattices, 417.

08. General Mathematical Systems


10. Number Theory

Berndt, Bruce C. A new proof of the functional equation of Dirichlet L-functions,

355.Brown, Ezra. Biquadratic reciprocity laws, 374.

Evans, Ronald J. Modular forms on Heche's modular groups, 411.

Suryanarayana, D. and Rao, R. Sita Rama Chandra. Distribution of semi-k-free

integers, 340.

12. Algebraic Number Theory, Field Theory and Polynomials

Rosenlicht, Maxwell. An analogue of VHospital's rule, 369.

13. Commutative Rings and Algebras

Alamelu, S. On commutativity of endomorphism rings of ideals, 29.

Arnold, J. T. and Brewer, J. W. When (D[[X]\)r^rXn is a valuation ring, 326.

Cowsik, R. C. On a question of M. Höchster, 75.

Gersten, S. M. K3 of a ring is H3 of the Steinberg group, 366.

Kuku, Aderemi O. Some algebraic K-theoretic applications of the LF and NF

functors, 363.

Pomfret, J. Similarity of matrices over finite rings, 421.

Roberts, Leslie G. An example of a Hilbert ring with maximal ideals of different

height, 425.

14. Algebraic Geometry

Eklof, Paul C. Lefschetz's principle and local functors, 333.

Ogus, Arthur. Zariski's theorem on several linear systems, 59.

15. Linear and Multilinear Algebra; Matrix Theory (finite and infinite)

Chung, I. Y. Direct decomposition of tensor products into subtensor products, 1.

de Oliveira, G. N. Matrices with prescribed entries and eigenvalues. I, 381.


625

626 INDEX TO VOLUME 37 [February

16. Associative Rings and Algebras

Chacron, M. and Chacron, J. Rings with involution all of whose symmetric elements

are nilpotent or regular, 397.


Michler, Gerhard O. The kernel of a block of a group algebra, 47.

Wehlen, Joseph A. Triangular matrix algebras over Hensel rings, 69.

18. Category Theory, Homological Algebra

Barr, Michael. Embedding of categories, 42.

Gersten, S. M. K, of a ring is Hz of the Steinberg group, 366.

Kuku, Aderemi O. Some algebraic K-theoretic applications of the LF and NF

functors, 363.20. Group Theory and Generalizations

Alperin, J. and Janusz, G. Resolutions and periodicity, 403.

Berger, T. R. Hall-Higman type theorems. IV, 317.

Boler, James and Evans, Benny. The free product of residually finite groupsamalgamated along retracts is residually finite, 50.

Groves, J. R. J. On direct products of regular p-groups, 377.

Herzog, Marcel. On Sylow intersections. 352.

Karrass, A. and Solitar, D. On finitely generated subgroups which are of finiteindex in generalized free products, 22.

Lady, E. L. Countable torsion products of abelian p-groups, 10.

Lorimer, Peter. A property of the groups PYL(m,q), q^S, 393.

Nico, William R. A property of projective ¡deals in semigroup algebras, 407.


Ribes, Luis. Amalgamated products of profinite groups: Counterexamples, 413.

Sehgal, Surinder K. Generalized projectors and Carter subgroups of finite groups,347.

Tang, C. Y. On the Frattini subgroups of certain generalized free products of

groups, 63.

Walker, Elbert A. Ulm's theorem for totally projective groups, 387.

Warne, R. J. On the structure of idempotent semigroups, 17.

B. Analysis

26. Real Functions

Adams, David R. and Polking, John C. The equivalence of two definitions of

capacity, 529.

Fadell, Albert. On the existence of regular approximate differentials, 541.

Helton, Jon C. Some interdependencies of sum and product integrals, 201.

Seeley, Robert T. Addendum to "Extension

of Cx functions defined in a half

space", 622.

Wilkins, J. Ernest, Jr. Bounds for the variational ratio of arbitrary linear systems,

128.28. Measure and Integration

Breckenridge, J. C. The significant cylindrical condition anda Hausdorff rectifiable

set, 549.Ridge, William C. Spectrum of a composition operator, 121.

Snell, Roy C. The range of invariant means on locally compact groups and semi-

groups, 441.

30. Functions of a Complex Variable

Behan, Donald F. Commuting analytic functions without fixed points, 114.

Gaier, Dieter. A note on Hall's lemma, 97.

1973] INDEX TO VOLUME 37 627

*Globevnik, J. and Vidav, I. A note on normal-operator-valued analytic functions,617.

Gresser, John T. The compactness of the set of arc cluster sets of an arbitrary

function, 195.

Herrero, Domingo A. Mean growth of inner functions, 175.

Metzger, Thomas A. On polynomial approximation in AQ(D), 468.

Miller, Sanford S., Mocanu, Petru and Reade, Maxwell O. All m-convex functionsare univalent and starlike, 553.

Nakki, Raimo and Palka, Bruce. Uniform equicontinuity of quasiconformalmappings, ATI.

Ow, Wellington H. PD-minimal solutions of \u = Pu on open Riemann surfaces,

85.Shaffer, Dorothy Browne. On bounds for the derivative of analytic functions, 517.

Sibner, R. J. An elementary proof of a theorem concerning infinitely connected

domains, 459.

Styer, D. and Wright, D. On the valence of the sum of two convex functions, 511.

31. Potential Theory

Adams, David R. and Polking, John C. The equivalence of two definitions of

capacity, 529.

Davis, Burgess. An inequality for the distribution of the Brownian gradient function,189.

McCoy, Peter A. Value distribution of potentials in three real variables, 471.

Ow, Wellington H. PD-minimal solutions of Au = Pu on open Riemann surfaces,

85.32. Several Complex Variables and Analytic Spaces

Chen, Su-shing. On a class of quasiconformal junctions in Banach spaces, 545.

Gilman, Jane. Compact Riemann surfaces with conformai involutions, 105.

34. Ordinary Differential Equations

Bownds, J. M. and Diaz, J. B. On restricted uniqueness for systems of ordinary

differential equations, 100.

Brown, R. C. and Krall, Allan M. Adjoints of multipoint-integral boundary value

problems, 213.

Dickey, R. W. A quasilinear evolution equation and the method of Galerkin,

149.

George, J. H. and York, R. J. Application of Liapunov theory to boundary value

problems. II, 207.

35. Partial Differential Equations

Ballou, Donald P. Weak solutions with unbounded variation, 181.

Diederich, J. R. Weyl's lemma for pointwise solutions of elliptic equations, 476.

Swanson, C. A. A comparison theorem for eigenfunctions, 537.*Uhlenbeck, K. A new proof of a regularity theorem for elliptic systems, 315.

40. Sequences, Series, Summability

Atalla, Robert E. Regular matrices and P-sets in ßN\N, 157.

42. Fourier Analysis

Blei, Ron C. On subsets with associated compacta in discrete abelian groups, 453.

43. Abstract Harmonic Analysis

Miller, John J. H. and Simms, D. J. On the coefficients of an asymptotic expansion

of spherical functions on symmetric spaces, 448.

Mueller-Roemer, Peter R. A tauberiangroup algebra, 163.

44. Integral Transforms, Operational Calculus



45. Integral Equations

Sours, Richard E. Absolutely continuous component of a class of integral operators,

521.46. Functional Analysis

Behncke, H. Nilpotent elements in Banach algebras, 137.

Busby, Robert C. On the equivalence of twisted group algebras and Banach*-algebraic bundles, 142.

Clancey, Kevin. Invariant subspaces of infinite codimension for some nonnormal

operators, 525.

Cochran, Allan C. Inductive limits of A-convex algebras, 489.

Davis, William J. and Johnson, William B. A renorming of nonreflexive Banach

spaces, 486.

Eifler, Larry Q. Inverting sets for function algebras, 96.

Howard, Joe. Mackey compactness in Banach spaces, 108.

Johnson, Gordon G. Inner products characterized by difference equations, 535.

Loy, R. J. Continuity of higher derivations, 505.McCharen, Edith A. A new topology on B*-algebras arising from the Arens

products, 77.-. A characterization of dual B*-algebras, 84.


Randtke, Daniel J. A simple example of a universal Schwartz space, 185.

Shields, Paul C. Weakly compact positive operators on summable functions, 456.

Sidney, S. J. A note on enveloped measures, 167.

Terzioglu, T. Smooth sequence spaces and associated nuclearity, 497.

Wong, Pak-Ken. On the Arens product and commutative Banach algebras, 111.

Woods, Paul Carlton. Markuschevich bases and semireflexivity, 217.

47. Operator Theory

Clancey, Kevin. Invariant subspaces of infinite codimension for some nonnormal

operators, 525.

Crandall, Michael G. A generalized domain for semigroup generators, 434.

Hochstadt, Harry. One dimensional perturbations of compact operators, 465.

Loy, R. J. Continuity of higher derivations, 505.

Okazawa, Noboru. Perturbations of linear M-accretive operators, 169.

Randtke, Daniel J. Representation theorems for compact operators, 481.

Ridge, William C. Spectrum of a composition operator, 121.


Sours, Richard E. Absolutely continuous component of a class of integral operators,

521.49. Calculus of Variations and Optimal Control

Silverman, Edward. A necessary condition in the calculus of variations, 462.

C. Applied Mathematics

68. Computer Science

Young, Paul. Easy constructions in complexity theory: Gap and speed-up theorems,

555.

D. Geometry50. Geometry

Lorimer, Peter. A property of the groups PTL(m, q), <7=£5, 393.

52. Convex Sets and Geometric Inequalities

Loveland, L. D. and Valentine, J. E. Convex metric spaces with O-dimensional

midsets, 568.

1973) INDEX TO VOLUME 37 629

53. Differential Geometry

Chen, Bang-yen. A characterization of standard flat tori, 564.

Gordon, William B. An analytical criterion for the completeness of riemannian

manifolds, 221.

E. Logic and Foundations

02. Logic and Foundations

Blass, Andreas. Determinateness and continuity, 572.


Young, Paul. Easy constructions in complexity theory: Gap and speed-up theorems

555.

F. Statistics and Probability

60. Probability Theory and Stochastic Processes


Hanson, D. L. and Wright, F. T. A theorem about the oscillation of sums of

independent random variables, 226.

Lange, Kenneth. Decompositions of substochastic transition functions, 575.

Rogge, Lothar. The convergence determining class of regular open sets, 581.

G. Topology

22. Topological Groups, Lie Groups

Lee, D. H. On the homomorphisms of locally compact groups, 246.

Snell, Roy C. The range of invariant means on locally compact groups and semi-

groups, 441.

54. General Topology

Chimenti, Frank A. Tychonoff's theorem for hyperspaces, 281.

Choe, Tae Ho. Injective compact distributive lattices, 241.

Friedler, Louis. Quotients of proximity spaces, 589.

Fuller, R. V. A characterization of local compactness, 615.

Gazik, R. J. A hyper space for convergence spaces, 234.

Hindman, Neil. Preimages of points under the natural map from ß(NxN) to

ßNxßN, 603.Hung, H. H. The amalgamation property for G-metric spaces, 53.

Loveland, L. D. and Valentine, J. E. Convex metric spaces with O-dimensional

midsets, 568.

Michael, E. and Nagami, K. Compact-covering images of metric spaces, 260.

Slaughter, F. G., Jr. The closed image of a metrizable space is Mx, 309.

55. Algebraic Topology

Boler, James and Evans, Benny. The free product of residually finite groupsamalgamated along retracts is residually finite, 50.

Chapman, T. A. Locally-trivial bundles and microbundles with infinite-dimensional

fibers, 595.Hardie, K. A. On composite loop functors, 586.

Heil, Wolfgang, ^-manifolds that are sums of solid tori and Seifert fiber spaces,

609.Wood, John C. A theorem on Injectivity of the cup product, 301.

57. Manifolds and Cell Complexes

Brown, Robert F. The real cohomology of compact disconnected Lie groups, 255.

Dieffenbach, Robert M. Homotopic PL n-balls are isotopic, Tl\.

630 INDEX TO VOLUME 37

Heil, Wolfgang. 2-manifolds that are sums of solid tori and Seifert fiber spaces,

609.Narvarte, J. A. A model for closed orientable 3-manifolds of genus 1, 287.

Porter, Richard D. An H-space with finite dimensional homology whose loop

space has torsion, 291.

Schochet, Claude. On the bordism ring of complex projective space, 267.

Wright, Perrin. Formal 3-deformations ofl-polyhedra, 305.

58. Global Analysis, Analysis on Manifolds

Franks, John. Absolutely structurally stable diffeomorphisms, 293.

Gordon, William B. Analytical criterion for the completeness of riemannian

manifolds, 221.

Plante, J. F. Homology of closed orbits of Anosov flows, 297.

AUTHOR INDEX

*Starred items are "Shorter

Notes"

Adams, David R. and Polking, John C. The equivalence of two definitions of capacity,

529.Alamelu, S. On commutativity of endomorphism rings of ideals, 29.

Alperin, J. and Janusz, G. Resolutions and periodicity, 403.

Arnold, J. T. and Brewer, J. W. When (D[[X]})PrrX^ is o valuation ring, 326.

Atalla, R. E. Regular matrices andP-sets in ßN\N, 157.

Ballou, Donald P. Weak solutions with unbounded variation, 181.

Barr, Michael. Embedding of categories, 42.

Behan, Donald F. Commuting analytic functions without fixed points, 114.

Behncke, H. Nilpotent elements in Banach algebras, 137.

Berger, T. R. Hall-Higman type theorems. IV, 317.

Berndt, Bruce C. A new proof of the functional equation of Dirichlet L-functions, 355.

Blass, Andreas. Determinateness and continuity, 572.

Blei, Ron C. On subsets with associated compacta in discrete abelian groups, 453.

Boler, James and Evans, Benny. The free product of residually finite groups amalgamated

along retracts is residually finite, 50.

Bownds, J. M. and Diaz, J. B. On restricted uniqueness for systems of ordinary differential

equations, 100.

Breckenridge, J. C. The significant cylindrical condition and a Hausdorff rectifiable set,

549.Brewer, J. W, See Arnold, J. T.

Brown, Ezra. Biquadratic reciprocity laws, 374.

Brown, R. C. and Krall, Allan M. Adjoints of multipoint-integral boundary value

problems, 213.

Brown, Robert F. The real cohomology of compact disconnected Lie groups, 255.

Busby, Robert C. On the equivalence of twisted group algebras and Banach *-algebraic

bundles, 142.

Chacron, J. and Chacron, M. Rings with involution all of whose symmetric elements are

nilpotent or regular, 397.

Chacron, M. See Chacron, J.

Chapman, T. A. Locally-trivial bundles and microbundles with infinite-dimensional fibers,595.

Chen, Bang-yen. A characterization of standard flat tori, 564.

Chen, Su-shing. On a class of quasiconformal functions in Banach spaces, 545.

Chimenti, Frank A. Tychonoff's theorem for hyperspaces, 281.

Choe, Tae Ho. Infective compact distributive lattices, 241.

Chung, I. Y. Direct decomposition of tensor products into subtensor products, 1.

Clancey, Kevin. Invariant subspaces of infinite codimension for some nonnormal operators,

525.Cochran, Allan C. Inductive limits of A-convex algebras, 489.

Cowsik, R. C. On a question of M. Höchster, 75.

Crandall, Michael G. A generalized domain for semigroup generators, 434.


631


Davis, William J. and Johnson, William B. A renorming of nonreflexive Banach spaces.

486.Diaz, J. B. See Bownds, J. M.

Dickey, R. W. A quasilinear evolution equation and the method ofGalerkin, 149.

Diederich, J. R. Weyl's lemma for pointwise solutions of elliptic equations, 476.

Dieffenbach, Robert M. Homotopic PL n-balls are isotopic, 271.

Eifler, Larry Q. Inverting sets for function algebras, 96.


Evans, Benny. See Boler, James.

Evans, Ronald J. Modular forms on Hecke's modular groups, 411.

Fadell, Albert. On the existence of regular approximate differentials, 541.

Franks, John. Absolutely structurally stable diffeomorphisms, 293.

Friedler, Louis. Quotients of proximity spaces, 589.

Fuller, R. V. A characterization of local compactness, 615.

Gaier, Dieter. A note on Hall's lemma, 97.

Gazik, R. J. A hyperspace for convergence spaces, 234.

George, J. H. and York, R. J. Application ofLiapunov theory to boundary value problems,II, 207.


Gilman, Jane. Compact Riemann surfaces with conformai involutions, 105.*Globevnik, J. and Vidav, I. A note on normal-operator-valued analytic functions,

617.Gordon, William B. An analytical criterion for the completeness ofriemannian manifolds,

221.Gresser, John T. The compactness of the set of arc cluster sets of an arbitrary function,

195.Groves, J. R. J. On direct products of regular p-groups, ill.

Hanson, D. L. and Wright, F. T. A theorem about the oscillation of sums of independent

random variables, 226.

Hardie, K. A. On composite loop functors, 586.

Heil, Wolfgang. 3-manifolds that are sums of solid tori and Seifert fiber spaces, 609.

Helton, Jon C. Some interdependencies of sum and product integrals, 201.

Herrero, Domingo A. Mean growth of inner functions, 175.

Herzog, Marcel. On Sylow intersections, 352.

Hindman, Neil. Preimages of points under the natural map from ß(NxN) to ßNxßN,603.

Hochstadt, Harry. One dimensional perturbations of compact operators, 465.

Howard, F. T. Formulas for the number of binomial coefficients divisible by a fixed powerof a prime, 358.

Howard, Joe. Mackey compactness in Banach spaces, 108.


Janusz, G. See Alperin, J.

Johnson, Gordon G. Inner products characterized by difference equations, 535.

Johnson, William B. See Davis, William J.

Karrass, A. and Solitar, D. On finitely generated subgroups which are of finite index in

generalized free products, 22.

Krall, Allan M. See Brown, R. C.Kuku, Aderemi O. Some algebraic K-theoretic applications of the LF and NF functors,

363.Lady, E. L. Countable torsion products of abelian p-groups, 10.

19731 INDEX TO VOLUME 37 633

Lakser, Harry. Principal congruences of pseudocomplemented distributive lattices, 32.

Lange, Kenneth. Decompositions of substochastic transition functions, 575.

Lee, D. H. On the homomorphisms of locally compact groups, 246.

Lorimer, Peter. A property of the groups PTL(m,q), q^5, 393.

Loveland, L. D. and Valentine, J. E. Convex metric spaces with O-dimensional midsets,

568.Loy, R. J. Continuity of higher derivations, 505.

McCharen, Edith A. A new topology of B*-algebras arising from the Arens products, 77.-. A characterization of dual B*-algebras, 84.


Metzger, Thomas A. On polynomial approximation in A„(D), 468.

Michael, E. and Nagami, K. Compact-covering images of metric spaces, 260.

Michler, Gerhard O. The kernel of a block of a group algebra, 47.Miller, John J. H. and Simms, D. J. On the coefficients of an asymptotic expansion of

spherical functions on symmetric spaces, 448.

Miller, Sanford S., Mocanu, Petru and Reade, Maxwell O. All a-convex functions are

univalent and starlike, 553.

Mocanu, Petru. See Miller, Sanford S.


Nagami, K. See Michael E.Näkki, Raimo and Palka, Bruce. Uniform equicontinuity of quasiconformal mappings,

427.Narvarte, J. A. A model for closed orientable 3-manifolds of genus 1, 287.

Nico, William R. A property of projective ideals in semigroup algebras, 407.

Ogus, Arthur. Zariski's theorem on several linear systems, 59.

Okazawa, Noboru. Perturbations of linear M-accretive operators, 169.

de Oliveira, G. N. Matrices with prescribed entries and eigenvalues. I, 381.*0'Neil, P. V. A short proof of Mac Lane's planarity theorem, 619.

Ow, Wellington H. PD-minimalsolutions ofAu=Pu on open Riemann surfaces, 85.

Palka, Bruce. See Näkki, Raimo.

Parker, E. T. Edge coloring numbers of some regular graphs, 423.

Plante, J. F. Homology of closed orbits of Anosov flows, 297.

Polking, John C. See Adams, David R.Pomfret, J. Similarity of matrices over finite rings, 421.

Porter, Richard D. An H-space with finite dimensional homology whose loop space has

torsion, 291.

Randtke, Daniel J. A simple example of a universal Schwartz space, 185.-. Representation theorems for compact operators, 481.

Rao, R. Sita Rama Chandra. See Suryanarayana, D.

Reade, Maxwell O. See Miller, Sanford S.

Reynolds, William H. A note on embedding a partially ordered ring in a division algebra,

37.Ribes, Luis. Amalgamated products of profinite groups: Counterexamples, 413.

Ridge, William C. Spectrum of a composition operator, 121.

Rival, Ivan. Maximal sublattices of finite distributive lattices, 417.

Roberts, Leslie G. An example of a Hilbert ring with maximal ideals of different height,

425.Rogge, Lothar. The convergence determining class of regular open sets, 581.

Rosenlicht, Maxwell. An analogue of VHospital's rule, 369.

Schochet, Claude. On the bordism ring of complex projective space, 267.

634 INDEX TO VOLUME 37

Seeley, Robert T. Addendum to "Extension of C" functions defined in a half space", 622.

Sehgal, Surinder K. Generalized projectors and Carter subgroups of finite groups, 347.

Shaffer, Dorothy Browne. On bounds for the derivative of analytic functions, 517.


Sibner, R. J. An elementary proof of a theorem concerning infinitely connected domains,

459.Sidney, S. J. A note on enveloped measures, 167.

Silverman, Edward. A necessary condition in the calculus of variations, 462.

Simms, D. J. See Miller, John J. H.Slaughter, F. G., Jr. The closed image of a metrizable space is Mly 309.

Snell, Roy C. The range of invariant means on locally compact groups and semigroups,

441.Solitar, D. See Karrass, A.

Sours, Richard E. Absolutely continuous component of a class of integral operators, 521.

Styer, D. and Wright, D. On the valence of the sum of two convex functions, 511.

Suryanarayana, D. and Rao, R. Sita Rama Chandra. Distribution of semi-k-free integers,

340.Swanson, C. A. A comparison theorem for eigenfunctions, 537.

Tang, C. Y. On the Frattini subgroups of certain generalized free products of groups, 63.

Terzioglu, T. Smooth sequence spaces and associated nuclearity, 497.•Uhlenbeck, K. A new proof of a regularity theorem for elliptic systems, 315.

Valentine, J. E. See Loveland, L. D.*Vidav, I. See Globevnik, J.

Walker, Elbert A. Ulm's theorem for totally projective groups, 387.

Warne, R. J. On the structure of idempotent semigroups, 17.

Wehlen, Joseph A. Triangular matrix algebras over Hensel rings, 69.

Wilkins, J. Ernest, Jr. Bounds for the variational ratio of arbitrary linear systems, 128.

Wong, Pak-Ken. On the Arens product and commutative Banach algebras, 111.

Wood, John C. A theorem on injectivity of the cup product, 301.

Woods, Paul Carlton. Markuschevich bases and semireflexivity, 217.

Wright, D. See Styer, D.

Wright, F. T. See Hanson, D. L.

Wright, Perrin. Formal 3-deformations ofl-polyhedra, 305.

York, R. J. See George, J. H.

Young, Paul. Easy constructions in complexity theory: Gap and speed-up theorems, 555.

VOLUME 37 NUMBERS 1-2 »(Si JANUARY- ÎRUARY 1973

§5Ü^ WHOLE NUMBERS 163-164

PROCEEDINGSJL OF THE

AMERICAN MATHEMATICAL SOCIETY

EDITED BYFred G. BrauerGlen E. BredonW. Wistar ComfortJacob Feldman

Richard R. GoldbergJoseph J. Rotman

George B. Seligman

With the Cooperation ofJay R. GoldmanJames D. KuelbsAllen L. ShieldsRobert I. Soare

PROVIDENCE, RHODE ISLAND USA

ISSN 0002-9939

Proceedings of the American Mathematical Society

This Journal is devoted entirely to research in pure and applied mathematics, andthe publication of original papers of moderate length. The maximum length of anacceptable paper is about 8 printed pages. Since a page of the Proceedings containsabout 400 words, a rule of thumb is that under 10 typed pages is probably within thelimit, but that over 12 typed pages is probably too long.

Shorter notes. Very short notes not to exceed 1 printed page of an unusual natureare also accepted, and appear under the heading Shorter Notes. Items deemed

suitable include an elegant new proof of an important and well-known theorem, an

illuminating example or counterexample, or a new viewpoint on familiar results. New

results, if of a brief and striking character, might also be acceptable, though in generala paper which is merely very short will not be suitable for the Shorter Notesdepartment.

Preparation of the manuscript. Articles for insertion should be typewritten anddouble spaced. Ditto is not generally satisfactory, although other modes of multiple

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Form of manuscript. The first page should consist of a descriptive title, followed byan abstract which summarizes the article in language suitable for workers in the generalfield (algebra, analysis, etc.). The descriptive title should be short, but informative;

useless or vague phrases such as "some remarks about" or

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avoided. Also avoid proper names unless mathematical usage associates them with

the work. The abstract should be at least one complete sentence, and at most 150words. Included with the footnotes to your paper, but placed before the first footnote,

there should be first the AMS (MOS) subject classification numbers representing the

primary and secondary subjects of the article. This may be followed by a list of keywords and phrases describing the subject matter of the article and taken from it. The

AMS (MOS) Subject Classification Scheme (1970) with instructions for its use can be

found as an appendix to Mathematical Reviews, Index to Volume 39 (June 1970). See

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Copyright © American Mathematical Society 1973

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10 9 8 7 6 5 4 3 2 01 00 99 98 97 (Number 1)

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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

CONTENTS*

Vol. 37, No. 1 JANUARY 1973 Whole No. 163

Page


Direct decomposition of tensor products into subtensor products. By I. Y.Chung. 1

Countable torsion products of abelian /»-groups. By E. L. Lady. 10On the structure of idempotent semigroups. By R. J. Warne. 17On finitely generated subgroups which are of finite index in generalized free prod-

ucts. By A. Karrass and D. Solttar. 22On commutativity of endomorphism rings of ideals. By S. Alamelu. 29Principal congruences of pseudocomplemented distributive lattices. By Harry

Lakser. 32A note on embedding a partially ordered ring in a division algebra. By William

H. Reynolds. 37Embedding of categories. By Michael Barr. 42The kernel of a block of a group albegra. By Gerhard O. Michler. 47The free product of residually finite groups amalgamated along retracts is residu-

ally finite. By James Boler and Benny Evans. 50The amalgamation property for G-metric spaces. By H. H. Hung. 53Zariski's theorem on several linear systems. By Arthur Ogus. 59On the Frattini subgroups of certain generalized free products of groups. By C. Y.

Tang. 63Triangular matrix algebras over Hensel rings. By Joseph A. Wehlen. 69On a question of M. Höchster. By R. C. Cowsik. 75

B. Analysis

A new topology on i?*-algebras arising from the Arens products. By Edith A.McCharen. 77

A characterization of dual B*-algebras. By Edith A. McCharen. 84jPZ)-minimal solutions of &u=Pu on open Riemann surfaces. By Wellington H.

Ow. 85Inverting sets for function algebras. By Larry Q. Eifler. 92A note on Hall's lemma. By Dieter Gaier. 97On restricted uniqueness for systems of ordinary differential equations. By J. M.

Bownds and J. B. Diaz. 100Compact Riemann surfaces with conformai involutions. By Jane Gilman. 105Mackey compactness in Banach spaces. By Joe Howard. 108On the Arens product and commutative Banach algebras. By Pak-Ken Wong .. IllCommuting analytic functions without fixed points. By Donald F. Behan ..... 114

Spectrum of a composition operator. By William C Ridge. 121

Bounds for the variational ratio of arbitrary linear systems. By J. Ernest Wilkins,Jr.,. 128

Nilpotent eiements in Banach algebras. By H. Behncke. 137

On the equivalence of twisted group algebras and Banach *-algebraic bundles. By

Robert C. Busby. 142A quasi-linear evolution equation and the method of Galerkin. By R. W. Dickey. 149

* The volume indexes contain a mapping showing the correspondence between

sections A-G and the AMS (MOS) subject classification numbers.

Regular matrices and P-sets in ßN\N. By R. E. Atalla. 157A tauberian group algebra. By Peter R. Mueller-Roemer. 163A note on enveloped measures. By S. J. Sidney. 167Perturbations of linear m-accretive operators. By Noboru Okazawa. 169Mean growth of inner functions. By Domingo A. Herrero. 175Weak solutions with unbounded variation. By Donald P. Ballou. 181A simple example of a universal Schwartz space. By Daniel J. Randtke. 185An inequality for the distribution of the Brownian gradient function. By Burgess

Davis. 189The compactness of the set of arc cluster sets of an arbitrary function. By John T.

Gresser. 195Some interdependences of sum and product integrals. By Jon C. Helton. 201Application of Liapunov theory to boundary value problems. II. By J. H. George

andR.J.York. 207Adjoints of multipoint-integral boundary value problems. By R. C. Brown and

Allan M. Krall. 213Markuschevich bases and semireflexivity. By Paul Carlton Woods. 217

D. Geometry

An analytical criterion for the completeness of riemannian manifolds. By WilliamB. Gordon. 221


A theorem about the oscillation of sums of independent random variables. ByD. L. Hanson and F. T. Wright._ 226

G. Topology

A hyperspace for convergence spaces. By R. J. Gazik. 234Injective compact distributive lattices. By Tae Ho Choe. 241On the homomorphisms of locally compact groups. By D. H. Lee. 246The real cohomology of compact disconnected Lie groups. By Robert F. Brown 255

Compact-covering images of metric spaces. By E. Michael and K. Nagami_ 260On the bordism ring of complex projective space. By Claude Schochet. 267Homotopic PL n-balls are isotopic. By Robert M. Dieffenbach. 271

Tychonoff's theorem for hyperspaces. By Frank A. Chimenti. 281

A model for closed orientable 3-manifolds of genus 1. By J. A. Narvarte. 287

An //-space with finite dimensional homology whose loop space has torsion. By

Richard D. Porter. 291Absolutely structurally stable diffeomorphisms. By John Franks. 293Homology of closed orbits of Anosov flows. By J. F. Plante. 297A theorem on injectivity of the cup product. By John C Wood. 301Formal 3-deformations of 2-polyhedra. By Perrin Wright._ 305The closed image of a metrizable space is Mx. By F. G. Slaughter, Jr. 309

Shorter Notes

A new proof of a regularity theorem for elliptic systems. By K. Uhlenbeck_ 315

Vol. 37, No. 2 FEBRUARY 1973 Whole No. 164

Page


Hall-Higman type theorems. IV. By T. R. Berger. 317

When (/>[[All)/>[[x]] is a valuation ring. By J. T. Arnold and J. W. Brewer. .. 326

Lefschetz's principle and local functors. By Paul C. Eklof. 333

Distribution of semi-£-free integere. By D. Suryanarayana and R. Sita RamaChandra Rao. 340

Generalized projectors and Carter subgroups of finite groups. By Surinder K.Sehgal. 347

On Sylow intersections. By Marcel Herzog. 352A new proof of the functional equation of Dirichlet ¿-functions. By Bruce C.

Berndt. 355Formulas for the number of binomial coefficients divisible by a fixed power of a

prime. By F. T. Howard. 358Some algebraic ^-theoretic applications of the LF and NF functors. By Aderemi

O. Kuku. 363K3 of a ring is H3 of the Steinberg group. By S. M. Gersten. 366An analogue of L'Hospital's rule. By Maxwell Rosenlicht. 369Biquadratic reciprocity laws. By Ezra Brown. 374On direct products of regular /»-groups. By J. R. J. Groves. 377Matrices with prescribed entries and eigenvalues. I. By G. N. de Oliveira. 380Ulm's theorem for totally projective groups. By Elbert A. Walker. 387A property of the groups PTL(m, q), q—S. By Peter Lorimer. 393Rings with involution all of whose symmetric elements are nilpotent or regular.

By J. Chacron and M. Chacron. 397Resolutions and periodicity. By J. Alperin and G. Janusz. 403A property of projective ideals in semigroup algebras. By William R. Nico_ 407Modular forms on Hecke's modular groups. By Ronald J. Evans. 411Amalgamated products of profinite groups: Counterexamples. By Luis Ribes ... 413Maximal sublattices of finite distributive lattices. By Ivan Rival. 417Similarity of matrices over finite rings. By J. Pomfret. 421Edge coloring numbers of some regular graphs. By E. T. Parker. 423An example of a Hilbert ring with maximal ideals of different height. By Leslie G.

Roberts. 425

B. Analysis

Uniform equicontinuity of quasiconformal mappings. By Raimo Näkki andBruce Palka. 427

A generalized domain for semigroup generators. By Michael G. Crandall_ 434The range of invariant means on locally compact groups and semigroups. By

Roy C Snell. 441On the coefficients of an asymptotic expansion of spherical functions on symmetric

spaces. By John J. H. Miller and D. J. Simms. 448On subsets with associated compacta in discrete abelian groups. By Ron C Blei 453Weakly compact positive operators on summable functions. By Paul C. Shields 456An elementary proof of a theorem concerning infinitely connected domains. By

R. J. Sibner. 459A necessary condition in the calculus of variations. By Edward Silverman_ 462One dimensional perturbations of compact operators. By Harry Hochstadt. .. 465On polynomial approximation in A,(D). By Thomas A. Metzger. 468

Value distribution of potentials in three real variables. By Peter A. McCoy_ 471Weyl's lemma for pointwise solutions of elliptic equations. By J. R. Diederich 476Representation theorems for compact operators. By Daniel J. Randtke. 481A renorming of nonreflexive Banach spaces. By William J. Davis and William B.

Johnson. 486Inductive limits of /4-convex algebras. By Allan C. Cochran. 489Smooth sequence spaces and associated nuclearity. By T. Terzioglu. 497Continuity of higher derivations. By R. J. Loy. 505On the valence of the sum of two convex functions. By D. Styer and D. Wright 511On bounds for the derivative of analytic functions. By Dorothy Browne Shaffer 517Absolutely continuous component of a class of integral operators. By Richard E.

Sours. 521Invariant subspaces of infinite codimension for some nonnormal operators. By

Kevin Clancey. 525The equivalence of two definitions of capacity. By David R. Adams and John C.

Polking. 529

Inner products characterized by difference equations. By Gordon G. Johnson 535A comparison theorem for eigenfunctions. By C. A. Swanson. 537On the existence of regular approximate differentials. By Albert Fadell. 541On a class of quasiconformal functions in Banach spaces. By Su-shing Chen ... 545The significant cylindrical condition and a Hausdorff rectifiable set. By J. C.

Breckenridge. 549All a-convex functions are univalent and starlike. By Sanford S. Miller, Petru

Mocanu and Maxwell O. Reade. 553

C. Applied Mathematics

Easy constructions in complexity theory: Gap and speed-up theorems. By PaulYoung. 555

D. Geometry

A characterization of standard flat tori. By Bang-yen Chen. 564Convex metric spaces with O-dimensional midsets. By L. D. Loveland and J. E.

Valentine. 568

E. Logic and Foundations

Determinateness and continuity. By Andreas Blass. 572


Decompositions of substochastic transition functions. By Kenneth Lange. 575The convergence determining class of regular open sets. By Lothar Rogge_ 581

G. Topology

On composite loop functors. By K. A. Hardie. 586

Quotients of proximity spaces. By Louis Friedler. 589Locally-trivial bundles and microbundles with infinite-dimensional fibers. By

T. A. Chapman. 595Preimages of points under the natural map from ß(NxN) to ßNxßN. By Neil

Hindman. 6033-manifolds that are sums of solid tori and Seifert fiber spaces. By Wolfgang Heil 609A characterization of local compactness. By R. V. Fuller. 615

Shorter Notes

A short proof of Mac Lane's planarity theorem. By P. V. O'Neil. 617A note on normal-operator-valued analytic functions. By J. Globevnik and

I.Vidav. 619Addendum to

"Extension of C°° functions defined in a half space". By Robert T.

Seeley. 622AMS (MOS) Major Subject Headings (1970). 623Index to Volume 37. 625

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